
Applying [1]} again, we may obtain
\(n(R_2-\delta ^{\prime }) &\le \sum _{i=1}^{n} \left[ I(W_2;Y_{2,i}|V^{\prime }_i)-I(W_2;Y_{3,i}|V^{\prime }_i)\right] \\&= \sum _{i=1}^{n} \left[ I(W_2,V^{\prime }_i;Y_{2,i})-I(W_2,V^{\prime }_i;Y_{3,i})\right]- \sum _{i=1}^{n} \left[ I(V^{\prime }_i;Y_{2,i})-I(V^{\prime }_i;Y_{3,i})\right] \\& \le \sum _{i=1}^{n} \left[ I(W_2,V^{\prime }_i;Y_{2,i})-I(W_2,V^{\prime }_i;Y_{3,i})\right] \) 
